The mathematics of cold Bose gas is one of the most extensively studied subject in mathematical physics recently. Many mathematically rigorous results have been obtained, mostly about its ground state energy and its dynamics in various models. In this talk, mathematical frameworks to study Bose gas will be introduced. Heuristics arguments and proofs to understand the properties of Bose gas, including the ground state energy of low-denstiy Bose gas and the rate of convergence towards Hartree dynamics, will also be explained.